Giga or gibi bytes?

If I run the df command on my current notebook, it tells me I have 141+8.1 giga

Filesystem Size Used Avail Use% Mounted on c: 141G 62G 80G 44% /cygdrive/c d: 8.1G 6.1G 2.0G 76% /cygdrive/d

That adds up to 149.1 gigabytes, quite a bit less than the 160GB stated in my machine’s specs.

But the truth is that hard drive manufacturers use the prefix giga correctly: it means 10 to the 9th power, a billion, or in figures 1,000,000,000.

Hard drive manufacturers use the prefix notation defined by the International Bureau of Weights and Measures. The International System of Units defines the prefixes for powers of 10:

  Factor  Prefix  Symbol  Factor  Prefix  Symbol
  10E24   yotta   Y       10E-24   yocto  y
  10E21   zetta   Z       10E-21   zepto  z
  10E18   exa     E       10E-18   atto   a
  10E15   peta    P       10E-15   femto  f
  10E12   tera    T       10E-12   pico   p
  10E9    giga    G       10E-9    nano   n
  10E6    mega    M       10E-6    micro  µ
  10E3    kilo    k       10E-3    milli  m
  10E2    hecto   h       10E-2    centi  c
  10E1    deca    da      10E-1    deci   d

So 160 gigabytes is 160E9 bytes, or 160,000,000,000 bytes.

But in computing tradition a gigabyte is 1024 megabytes, a megabyte is 1024 kilobytes, and those in turn are 1024 bytes each. Since everything is expressed in powers of 2, a kilobyte was 2 to the 10th, a mega 2 to the 20th, and a gigabyte 2 to the 30th.

Operating systems, and the tools that work with hard drives (like the df command), follow this custom: everything is expressed in powers of 2, but using the prefixes of the decimal system.

To avoid confusion the IEEE defined the IEEE-1541 standard, which was included in IEC 60027, the International Electrotechnical Commission standard that defines the symbols and letters used in electronics.

This standard defines new prefixes for powers of 2:

  kibibyte  KiB   2e10
  mebibyte  MiB   2e20
  gibibyte  GiB   2e30
  tebibyte  TiB   2e40
  pebibyte  PiB   2e50
  exbibyte  EiB   2e60
  zebibyte  ZiB   2e70
  yobibyte  YiB   2e80

• Here I used the notation 2eXX to mean 2 to the power of XX.

Therefore my 160 gigabyte hard drive has a capacity of 149.1 gibibytes.

Although the abbreviations are used in some publications and software, adoption of this standard is low, and as Jeff Atwood points out, the reasons would be that the prefixes sound ridiculous, hard drive manufacturers don’t use them, and tradition prevails.

This confusion over how to state hard drive sizes has led to some rather notorious lawsuits, and many users get upset when they buy a hard drive, look at it from their operating system and notice they have “lost” a lot of megabytes. These days, with hard drives over 80 gigabytes, the difference between what the manufacturer states and what the operating system reports can reach 7%.